Finite Group Databasebeta

← #77160

Subgroups — #77160

Order 384.

578 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#884C211yesmaximal, characteristic, complemented
2C2×#883C211yesmaximal, characteristic, complemented
3C3×#394C211yesmaximal, characteristic, complemented
4#5223C211yesmaximal, characteristic, complemented
5#5223C211yesmaximal, characteristic, complemented
6#4994C211yesmaximal, characteristic, complemented
7#4987C211yesmaximal, characteristic, complemented
8#4961C211yesmaximal, characteristic, complemented
9#4961C211yesmaximal, characteristic, complemented
10#4961C211yesmaximal, characteristic, complemented
11#4960C211yesmaximal, characteristic, complemented
12#4949C211yesmaximal, characteristic, complemented
13#4948C211yesmaximal, characteristic, complemented
14#4672C211yesmaximal, characteristic, complemented
15#4660C211yesmaximal, characteristic, complemented
16#2813—31nomaximal, Sylow
17C22×C3×D4C2211yescharacteristic
18C22×#67C2211yescharacteristic
19C22×#67C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C22×D12C2211yescharacteristic
23C22×C4×D3C2211yescharacteristic
24C2×C3×C4⋊C4C2211yescharacteristic
25C2×C3×C22⋊C4C2211yescharacteristic
26C2×C3×C22⋊C4C2211yescharacteristic
27C2×C3×C22⋊C4C2211yescharacteristic
28C2×C3×C22⋊C4C2211yescharacteristic
29C2×#217C2211yescharacteristic
30C2×#217C2211yescharacteristic
31C2×#217C2211yescharacteristic
32C2×#217C2211yescharacteristic
33C2×(C2×D3)⋊C4C2211yescharacteristic
34C2×(C2×D3)⋊C4C2211yescharacteristic
35C2×(C2×D3)⋊C4C2211yescharacteristic
36C2×(C2×D3)⋊C4C2211yescharacteristic
37C2×(C2×D3)⋊C4C2211yescharacteristic
38C2×(C2×D3)⋊C4C2211yescharacteristic
39C2×(C2×D3)⋊C4C2211yescharacteristic
40C2×C4⋊Dic3C2211yescharacteristic
41C2×C4⋊Dic3C2211yescharacteristic
42C2×C4⋊Dic3C2211yescharacteristic
43C2×Dic3⋊C4C2211yescharacteristic
44C2×Dic3⋊C4C2211yescharacteristic
45C2×Dic3⋊C4C2211yescharacteristic
46#884—24no—
47#883—24no—
48C3×#95C2211yescharacteristic
49C3⋊#95C2211yescharacteristic
50C3⋊#95C2211yescharacteristic
51C3⋊#95C2211yescharacteristic
52C3⋊#95C2211yescharacteristic
53C3⋊#95C2211yescharacteristic
54C2×#123—31no—
55C2×#121—31no—
56#400—31no—
57#399—31no—
58#396—31no—
59#396—31no—
60#394—31no—
61#394—31no—
62#394—31no—
63#394—31no—
64#394D311yescharacteristic, complemented
65#392—31no—
66#392—31no—
67#392—31no—
68#380—31no—
69C24×C3C2311yescharacteristic
70C24×C3C2311yescharacteristic
71C23×D3C2311yescharacteristic
72C23×D3C2311yescharacteristic
73C2×C3×D4—41no—
74C2×C3×D4—41no—
75C2×C3×D4—41no—
76C22×C3×C4C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C22×C3×C4C2311yescharacteristic
79C22×C3×C4C2311yescharacteristic
80C22×C3×C4C2311yescharacteristic
81C2×#67—22no—
82C2×#67—22no—
83C2×#67—22no—
84C2×#67—41no—
85C2×#67—41no—
86C2×#67—41no—
87C2×#67—41no—
88C2×#67—41no—
89C2×#67—41no—
90C2×#67—41no—
91C2×#67—41no—
92C2×#67—41no—
93C22×Dic3C2311yescharacteristic
94C22×Dic3C2311yescharacteristic
95C22×Dic3C2311yescharacteristic
96C22×Dic3C2311yescharacteristic
97C22×Dic3C2311yescharacteristic
98C22×Dic3C2311yescharacteristic
99C2×D12—22no—
100C2×D12—41no—
101C2×D12—41no—
102C2×C4×D3—41no—
103C2×C4×D3—41no—
104C2×C4×D3D414yescomplemented
105C3×C4⋊C4—41no—
106C3×C22⋊C4—22no—
107C3×C22⋊C4—22no—
108C3×C22⋊C4—41no—
109C3×C22⋊C4—41no—
110#217—22no—
111#217—41no—
112#217—41no—
113#217—41no—
114(C2×D3)⋊C4—22no—
115(C2×D3)⋊C4—22no—
116(C2×D3)⋊C4—41no—
117(C2×D3)⋊C4—41no—
118(C2×D3)⋊C4—41no—
119(C2×D3)⋊C4—41no—
120(C2×D3)⋊C4—41no—
121C4⋊Dic3—22no—
122C4⋊Dic3—41no—
123C4⋊Dic3—41no—
124Dic3⋊C4—22no—
125Dic3⋊C4—22no—
126Dic3⋊C4—41no—
127C22×D4—31no—
128C22×D4—31no—
129C22×D4—31no—
130C22×D4—31no—
131C22×D4—31no—
132C22×D4C2×D311yescharacteristic
133C23×C4—31no—
134#123—64no—
135#121—64no—
136C2×C4⋊C4—31no—
137C2×C4⋊C4—31no—
138C2×C4⋊C4—31no—
139C2×C4⋊C4—31no—
140C2×C4⋊C4—31no—
141C2×C4⋊C4—31no—
142C2×C4⋊C4C2×D311yescharacteristic
143C2×C22⋊C4—31no—
144C2×C22⋊C4—31no—
145C2×C22⋊C4—31no—
146C2×C22⋊C4—31no—
147C2×C22⋊C4—31no—
148C2×C22⋊C4—31no—
149C2×C22⋊C4—31no—
150C2×C22⋊C4—31no—
151C2×C22⋊C4—31no—
152C2×C22⋊C4—31no—
153C2×C22⋊C4—31no—
154C2×C22⋊C4C2×D311yescharacteristic
155C2×C22⋊C4C2×D311yescharacteristic
156C2×C22⋊C4C2×D311yescharacteristic
157C2×C22⋊C4C2×D311yescharacteristic
158#95—31no—
159#95—31no—
160#95—31no—
161#95—31no—
162#95—31no—
163#95C2×D311yescharacteristic
164C23×C3—21no—
165C23×C3—21no—
166C23×C3—21no—
167C23×C3—21no—
168C23×C3—21no—
169C23×C3—21no—
170C23×C3—21no—
171C23×C3—21no—
172C23×C3—21no—
173C23×C3—21no—
174C23×C3—21no—
175C23×C3—21no—
176C23×C3—21no—
177C23×C3—21no—
178C23×C3C2411yescharacteristic
179C22×D3—21no—
180C22×D3—21no—
181C22×D3—21no—
182C22×D3—21no—
183C22×D3—21no—
184C22×D3—21no—
185C22×D3—21no—
186C22×D3—21no—
187C22×D3—21no—
188C22×D3—21no—
189C22×D3—21no—
190C22×D3—21no—
191C22×D3—21no—
192C22×D3C2×D412yes—
193C3×D4—44no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4C2×D412yes—
209#67—44no—
210#67—44no—
211#67—44no—
212#67—44no—
213C2×Dic3—21no—
214C2×Dic3—21no—
215C2×Dic3—21no—
216C2×Dic3—21no—
217C2×Dic3—21no—
218C2×Dic3—21no—
219C2×Dic3—21no—
220C2×Dic3—21no—
221C2×Dic3—21no—
222C2×Dic3—21no—
223C2×Dic3—21no—
224C2×Dic3—21no—
225C2×Dic3—21no—
226C2×Dic3—21no—
227C2×Dic3—21no—
228C2×Dic3—21no—
229C2×Dic3—21no—
230C2×Dic3C2×D412yes—
231D12—44no—
232C4×D3—44no—
233C24—31no—
234C24—31no—
235C24C22×D311yescharacteristic
236C24C22×D311yescharacteristic
237C2×D4—41no—
238C2×D4—41no—
239C2×D4—41no—
240C2×D4—62no—
241C2×D4—62no—
242C2×D4—62no—
243C2×D4—62no—
244C2×D4—121no—
245C2×D4—121no—
246C2×D4—121no—
247C2×D4—121no—
248C2×D4—121no—
249C2×D4—121no—
250C2×D4—121no—
251C2×D4—121no—
252C2×D4—121no—
253C2×D4—121no—
254C2×D4—121no—
255C22×C4—31no—
256C22×C4—34no—
257C22×C4—31no—
258C22×C4—31no—
259C22×C4—31no—
260C22×C4—31no—
261C22×C4—31no—
262C22×C4—121no—
263C22×C4—121no—
264C22×C4C22×D311yescharacteristic
265C22×C4C22×D311yescharacteristic
266C22×C4C22×D311yescharacteristic
267C22×C4C22×D311yescharacteristic
268C22×C4C22×D311yescharacteristic
269C4⋊C4—41no—
270C4⋊C4—62no—
271C4⋊C4—62no—
272C4⋊C4—62no—
273C4⋊C4—121no—
274C4⋊C4—121no—
275C4⋊C4—121no—
276C22⋊C4—22no—
277C22⋊C4—22no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—62no—
281C22⋊C4—62no—
282C22⋊C4—62no—
283C22⋊C4—121no—
284C22⋊C4—121no—
285C22⋊C4—121no—
286C22⋊C4—121no—
287C22⋊C4—121no—
288C22⋊C4—121no—
289C22⋊C4—121no—
290C22⋊C4—121no—
291C22×C3—41no—
292C22×C3—41no—
293C22×C3—41no—
294C22×C3—41no—
295C22×C3—41no—
296C22×C3—41no—
297C22×C3—41no—
298C22×C3—41no—
299C22×C3—41no—
300C22×C3—41no—
301C22×C3—41no—
302C22×C3—41no—
303C22×C3—41no—
304C22×C3—41no—
305C22×C3C22×D411yescharacteristic
306C22×C3H(5,𝔽2)11yescharacteristic
307C22×C3H(5,𝔽2)11yescharacteristic
308C22×C3H(5,𝔽2)11yescharacteristic
309C22×C3H(5,𝔽2)11yescharacteristic
310C22×C3H(5,𝔽2)11yescharacteristic
311C22×C32−1+411yescharacteristic
312C2×D3—22no—
313C2×D3—22no—
314C2×D3—22no—
315C2×D3—41no—
316C2×D3—41no—
317C2×D3—41no—
318C2×D3—41no—
319C2×D3—41no—
320C2×D3—41no—
321C2×D3—41no—
322C2×D3—41no—
323C2×D3—41no—
324C2×D3—41no—
325C2×D3—41no—
326C3×C4—22no—
327C3×C4—41no—
328C3×C4—41no—
329C3×C4—41no—
330C3×C4—41no—
331Dic3—22no—
332Dic3—41no—
333Dic3—41no—
334Dic3—41no—
335Dic3—41no—
336Dic3—41no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—32no—
352C23—61no—
353C23—61no—
354C23—61no—
355C23—61no—
356C23—61no—
357C23—61no—
358C23—61no—
359C23—61no—
360C23—61no—
361C23—61no—
362C23—61no—
363C23—61no—
364C23—61no—
365C23C23×D311yescharacteristic
366D4—44no—
367D4—124no—
368D4—124no—
369D4—124no—
370D4—124no—
371D4—124no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—32no—
387C2×C4—61no—
388C2×C4—61no—
389C2×C4—61no—
390C2×C4—61no—
391C2×C4—61no—
392C2×C4—61no—
393C2×C4—61no—
394C2×C4—61no—
395C2×C4—61no—
396C2×C4—61no—
397C2×C4—61no—
398C2×C4—61no—
399C2×C4—61no—
400C2×C4—61no—
401C2×C4—61no—
402C2×C4—61no—
403C2×C4—61no—
404C2×C4—124no—
405C2×C4D3×D412yes—
406C2×C3—81no—
407C2×C3—81no—
408C2×C3#53411yescharacteristic
409C2×C3#53511yescharacteristic
410C2×C3#53711yescharacteristic
411C2×C3#56011yescharacteristic
412C2×C3#56011yescharacteristic
413C2×C3#56211yescharacteristic
414C2×C3#56211yescharacteristic
415D3—42no—
416D3—81no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—62no—
432C22—62no—
433C22—62no—
434C22—121no—
435C22—121no—
436C22—121no—
437C22—121no—
438C22—121no—
439C22—121no—
440C22—121no—
441C22—121no—
442C22—121no—
443C22—121no—
444C22—121no—
445C22C2×D3×D411yescharacteristic
446C22#100411yescharacteristic
447C22#100411yescharacteristic
448C22#100411yescharacteristic
449C22#100911yescharacteristic
450C22#100911yescharacteristic
451C22#101011yescharacteristic
452C4—22no—
453C4—41no—
454C4—41no—
455C4—41no—
456C4—41no—
457C4—62no—
458C4—121no—
459C4—121no—
460C4—121no—
461C4—121no—
462C4—121no—
463C3#281311yescharacteristic, complemented, Sylow
464C2—81no—
465C2—81no—
466C2—122no—
467C2—241no—
468C2#559511yescharacteristic
469C2#560511yescharacteristic
470C2#560711yescharacteristic
471C2#560811yescharacteristic
472C2#566611yescharacteristic
473C2#566711yescharacteristic
474C2#568411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#394C2
hypercenter#394D3
hypocenterC3#2813
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #394

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#884C2semidirect
2. C2×#883C2semidirect
3. C3×#394C2semidirect
4. #5223C2semidirect
5. #5223C2semidirect
6. #4994C2semidirect
7. #4987C2semidirect
8. #4961C2semidirect
9. #4961C2semidirect
10. #4961C2semidirect
11. #4960C2semidirect
12. #4949C2semidirect
13. #4948C2semidirect
14. #4672C2semidirect
15. #4660C2semidirect
64. #394D3semidirect
104. C2×C4×D3D4semidirect
463. C3#2813semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#8842
C2×#8832
C3×#3942
#52232
#49942
#49872
#49612
#49602
#49492
#49482
#46722
#46602
#28133